2025/08/05 by Carlos Heredia, Carlos Heredia Pimienta, Josep Llosa +2
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Nonlinear Photonic Systems
paper · pdf · doi:10.1088/1751-8121/ae8b5e
Abstract We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a trajectory-based variational principle and a generalized Noether theorem, we define the canonical momenta and energy. Moreover, we construct a (pre)symplectic form on the kinematic space, and show that its restriction to the phase space yields a true (pre)symplectic structure encoding the dynamics. Three examples—a finite nonlocal oscillator, the fully nonlocal Pais–Uhlenbeck model, and a delayed harmonic oscillator—demonstrate how phase space and the Hamiltonian emerge without explicitly solving the Euler–Lagrange equations.